How do you sketch a right triangle corresponding to sectheta=2 and find the third side, then find the other five trigonometric functions?

1 Answer
MathFact-orials.blogspot.com
Dec 25, 2016

See below:

Explanation:

With a triangle with sectheta=2, let's first remember that:

sectheta="hypotenuse"/"adjacent"=2/1

We could run through the pythagorean theorem for the third side, but we can also remember that these two measurements are part of a 30-60-90 triangle, and so the third side is sqrt3. To prove it, let's go ahead and do Pythagorean Theorem:

a^2+b^2=c^2

1^2+(sqrt3)^2=2^2

1+3=4

This gives us the 6 trig ratios:

sintheta=sqrt3/2

costheta=1/2

tantheta=(sqrt3/2)/(1/2)=(sqrt3/2)(2/1)=sqrt3

csctheta=2/sqrt3=(2sqrt3)/3

sectheta=2/1=2

cottheta=1/sqrt3=sqrt3/3

The angle of the triangle we're looking at is 60=pi/3, with the opposite being the middle length of sqrt3, the adjacent length of 1, and hypotenuse of 2.

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